5th round fixture

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If it’s like the cup draw where ALL 16 balls get drawn, then everyone’s entering, everyone will definitely win and the club will go bankrupt.
No they won't because there can only be 8 winners. As once two balls have come out these are discarded. But if you pick ball number 1 you have choice of picking it with 15 other numbers but it can only come out with 1 other. Same with number 2 etc.
 

Or to calculate the probability using the permutations logic, we need to work out the number of permutations that include us against Weds divided by the total number of possible draws without that restriction, so:

- number of combinations that put us together: There are 8 draws that will put us together 1&2, 3&4 etc and each can be reversed (United 1st or United 2nd) and we need to times this by 14! (14*13*12 etc), which is the number of possible orders for the other 14 clubs in the draw once we know one pair is us vs Weds;

- divided by the number of combinations of all possible draws, which is just 16!

This gives (0.067 or 1 in 15).
Again you are failing to take into account that if they are drawn 3rd and 4th then they can't come out 1st and 2nd, for example.
 
That is explained much further up. You have 16 balls in a hat. Means you have a 2/16 chance of you or opponent you want coming out first and a 1/15 chance coming out 2nd. 1/15 x 2/16 = 2/240 or 1/120. If you want to add it up its 15+14+13+12 etc for combinations.
Ok, my 15 are
Manchester United
Chelsea
Southampton or Tottenham Hotspur
Sheffield Wednesday
AFC Bournemouth or Arsenal
Northampton Town or Derby County
Leicester City
Reading or Cardiff City
West Bromwich Albion
Norwich City
Coventry City or Birmingham City
Manchester City
Newcastle United or Oxford United
Portsmouth
Shrewsbury Town or Liverpool

What are your other 105?
 
No they won't because there can only be 8 winners. As once two balls have come out these are discarded. But if you pick ball number 1 you have choice of picking it with 15 other numbers but it can only come out with 1 other. Same with number 2 etc.
So do you think that when they draw the lottery if you get the first six numbers you win, then they carry on drawing numbers and if you get numbers 7-12 you also win, and so on until they run out of balls?
 
Ok, my 15 are
Manchester United
Chelsea
Southampton or Tottenham Hotspur
Sheffield Wednesday
AFC Bournemouth or Arsenal
Northampton Town or Derby County
Leicester City
Reading or Cardiff City
West Bromwich Albion
Norwich City
Coventry City or Birmingham City
Manchester City
Newcastle United or Oxford United
Portsmouth
Shrewsbury Town or Liverpool

What are your other 105?
15 if you United come out of the hat first. But what if Chelsea come out first for instance. There are 120 permutations of fixtures.
 
Again you are failing to take into account that if they are drawn 3rd and 4th then they can't come out 1st and 2nd, for example.


Any other team than us and them being drawn 1st in the 1st, 3rd, 5th and 7th draws must affect the odds of a Derby match because of the chance of one of us being drawn second in each two team draw, as soon as the first team drawn is known?
 
I've just done a draw and we get Man U at home. Wednesday get Coventry/Birmingham at home


Don't bother with The One Show
 
Again you are failing to take into account that if they are drawn 3rd and 4th then they can't come out 1st and 2nd, for example.

I’m really not.

In a semi-final draw what do you think the probability would be out of curiosity? I’m assuming 2/4 * 1/3 = 1/6 based on what you’ve done this time.

If so, write out a list and see if you get my answer that there’s actually 8 out of 24 = 1/3 draws that give a Derby.
 
Again you are failing to take into account that if they are drawn 3rd and 4th then they can't come out 1st and 2nd, for example.
Okay so I don't post much on here but since we're doing maths, I'm right in my element. Forget about which order the draw comes out and who's home and away, the total of all probabilities is 1 since we must get drawn. There are only 15 possible outcomes if we're only talking about which team we will face. Now unless you want to try and tell me that we have a greater chance of drawing Portsmouth than Wednesday then the probability of us facing Wednesday is 1 in 15. If you still think that the draw mechanics affects this probability then I can draw you out a big probability tree diagram we used to do at school for the whole draw including the mechanics in the morning.
 
Okay so I don't post much on here but since we're doing maths, I'm right in my element. Forget about which order the draw comes out and who's home and away, the total of all probabilities is 1 since we must get drawn. There are only 15 possible outcomes if we're only talking about which team we will face. Now unless you want to try and tell me that we have a greater chance of drawing Portsmouth than Wednesday then the probability of us facing Wednesday is 1 in 15. If you still think that the draw mechanics affects this probability then I can draw you out a big probability tree diagram we used to do at school for the whole draw including the mechanics in the morning.
It was not the chances of us drawing Wednesday, it was the chances of us and Wednesday playing each other in the draw. Completely different question.
 
It was not the chances of us drawing Wednesday, it was the chances of us and Wednesday playing each other in the draw. Completely different question.
I believe us drawing Wednesday and us and Wednesday playing eachother in the draw is the same outcome. I'm going to put together a nice way of showing all the possible outcomes for us and I can guarantee you that 1 in 15 of them will have us and Wednesday playing eachother in the draw.
 
I believe us drawing Wednesday and us and Wednesday playing eachother in the draw is the same outcome. I'm going to put together a nice way of showing all the possible outcomes for us and I can guarantee you that 1 in 15 of them will have us and Wednesday playing eachother in the draw.
Here's a spreadsheet that shows every possible outcome with "O" representing other, there are 240 possible outcomes and 16 of them have us and Wednesday playing eachother in the draw. Hope everyone's happy now.



Yes it is extremely sad that I've spent this time at 2 in the morning making a spreadsheet to prove/show probabilities on a football forum. ;)
 

Here's a spreadsheet that shows every possible outcome with "O" representing other, there are 240 possible outcomes and 16 of them have us and Wednesday playing eachother in the draw. Hope everyone's happy now.



Yes it is extremely sad that I've spent this time at 2 in the morning making a spreadsheet to prove/show probabilities on a football forum. ;)

Far from it!
 
Mick who sits next to me on the Kop shares the same birthday as me. What were the chances of that happening before our randomly purchased season tickets sat us next to each other in 2006?
8,030,000 to 1 that’s the chance of that happening. Did you have a tenner on it. That’s supposing we had 22000 season tickets sold that year . Last prem year was it.
 
8,030,000 to 1 that’s the chance of that happening. Did you have a tenner on it. That’s supposing we had 22000 season tickets sold that year . Last prem year was it.

It was that season yes. However, I doubt I'll be renewing next season as this thread has forced me to hang myself.
 
Apologies if I've missed it discussed properly somewhere - I got lost in the odds of drawing Team X discussion - but is there a genuine chance of our game v Norwich on 7th March being moved? I assumed if the 5th round being played mid-week was an accepted part of the calendar that there would be no need to shift any games.

Asking as someone who's already booked return tickets to Sheffield for that game 😅
 
Apologies if I've missed it discussed properly somewhere - I got lost in the odds of drawing Team X discussion - but is there a genuine chance of our game v Norwich on 7th March being moved? I assumed if the 5th round being played mid-week was an accepted part of the calendar that there would be no need to shift any games.

Asking as someone who's already booked return tickets to Sheffield for that game 😅
Yes, ties are to be played Tues, Weds and Thursday, so if either us or Norwich play on the Thursday night then I presume our league game against Norwich will be put back to Sun 8 March.
 
Yes, ties are to be played Tues, Weds and Thursday, so if either us or Norwich play on the Thursday night then I presume our league game against Norwich will be put back to Sun 8 March.

Oh, brilliant. Thought once we'd got the all-clear from Sky it'd be fine 🤦‍♂️
 
How much did you have to drink last night Mobile? 🤣

Now that Toby's written out every possible outcome for you are you happy that the chance of us drawing one of fifteen teams is... 1 in 15?
 
If Mobile blade is so confident of his maths perhaps he would be prepared to bet me on it. i will accept, generously compared to the 120 to 1 he thinks it is, 60 to 1 odds of Utd being drawn against Wenesday. The only proviso is that we have to bet with same odds on all the other 15 teams too.

I will donate my winnings to the upkeep of this site.
 
Here's the full calculation.

Probability of Sheffield Derby = P(sd)
Probability of Sheffield Derby as Tie 1 P(t1)... etc
Probability of drawing Sheffield club = P(s)
Probability of drawing any other club = P(o)

We'll take the probability of each ball in order giving us the outcome of a Sheffield Derby until we get the two clubs out together, so P(t) = P(b1) x P(b2) x P(b3), etc. We could do all 16 balls each time, but once we have both Sheffield clubs out then we're just left with P(o) = 1 for the remaining balls.

Here's the really tedious bit:

P(t1) = P(s) x P(s) = 2/16 x 1/15 = 2/240 = 1/120
P(t2) = P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 2/14 x 1/13 = 364/43,680 = 1/120
P(t3) = P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 2/12 x 1/11 = 48,048/5,765,760 = 1/120
P(t4) = P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 10/12 x 9/11 x 2/10 x 1/9 = 4,324,320/518,918,400 = 1/120
(the multiplied fractions are getting silly now, so I'll skip to the simplest fraction, and I think we can see a pattern emerging)
P(t5) = P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 10/12 x 9/11 x 8/10 x 7/9 x 2/8 x 1/7 = 1/120
P(t6) = P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 10/12 x 9/11 x 8/10 x 7/9 x 6/8 x 5/7 x 2/6 x 1/5 = 1/120
P(t7) = P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 10/12 x 9/11 x 8/10 x 7/9 x 6/8 x 5/7 x 4/6 x 3/5 x 2/4 x 1/3 = 1/120
P(t8) = P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(o) x P(s) x P(s) = 14/16 x 13/15 x 12/14 x 11/13 x 10/12 x 9/11 x 8/10 x 7/9 x 6/8 x 5/7 x 4/6 x 3/5 x 2/4 x 1/3 x 2/2 x 1/1 = 1/120

P(sd) = P(t1) + P(t2) + P(t3) + P(t4) + P(t5) + P(t6) + P(t7) + P(t8)
P(sd) = 1/120 + 1/120 + 1/120 + 1/120 + 1/120 + 1/120 + 1/120 + 1/120
P(sd) = 8/120
P(sd) = 1/15

If anyone wants to argue further that it is anything other than 1/15 then there really is no hope.
 
But what happens if, say, Liverpool are drawn out of the hat first? Don't our odds of playing Wednesday decrease?
 

Ok, my 15 are
Manchester United
Chelsea
Southampton or Tottenham Hotspur
Sheffield Wednesday
AFC Bournemouth or Arsenal
Northampton Town or Derby County
Leicester City
Reading or Cardiff City
West Bromwich Albion
Norwich City
Coventry City or Birmingham City
Manchester City
Newcastle United or Oxford United
Portsmouth
Shrewsbury Town or Liverpool

What are your other 105?

I was going to do this but couldn't be arsed. So thanks for making the effort :-)
 

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